How prepared should a baked dessert be before a long transport?

Assuming you really do a crisp/cobbler, you can do any of those. If having it fresh and hot is the most important thing, but you want to avoid the inconvenience of cooking too much at your destination, your best choice is to prep first and cook later. (This all changes completely if you decide to bake a cake instead.)

Assuming you like it served hot, it'll of course be best if it's cooked there. You might as well do the prep first (but of course you don't have to); just be sure to keep the topping and the fruit separate and assemble right before baking so it doesn't all soak through.

Doing it all beforehand is probably the most convenient though, and it'll work fine. You can reheat it in the oven at your destination; that should help crisp up the topping a bit. (You might want to err on the side of underbrowning it at home, though, so you don't burn the top later. You can also cover it with foil to keep it from overbrowning.) And of course, if you don't want to serve it hot anyway, you might as well do it all at home.